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On the super-additivity and estimation biases of quantile contributions

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  • Taleb, Nassim Nicholas
  • Douady, Raphael

Abstract

Sample measures of top centile contributions to the total (concentration) are downward biased, unstable estimators, extremely sensitive to both sample and population size and concave in accounting for large deviations. It makes them particularly unfit in domains with power law tails, especially for low values of the exponent. These estimators can vary over time and increase with the population size, thus providing the illusion of structural changes in concentration. They are also inconsistent under aggregation and mixing distributions, as the weighted average of concentration measures for A and B will tend to be lower than that from A∪B. In addition, it can be shown that under such fat tails, increases in the total sum need to be accompanied by increased sample size of the concentration measurement. We examine the estimation superadditivity and bias under homogeneous and mixed distributions.

Suggested Citation

  • Taleb, Nassim Nicholas & Douady, Raphael, 2015. "On the super-additivity and estimation biases of quantile contributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 429(C), pages 252-260.
    • Handle: RePEc:eee:phsmap:v:429:y:2015:i:c:p:252-260
    DOI: 10.1016/j.physa.2015.02.038
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    1. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    2. Dagum, Camilo, 1980. "Inequality Measures between Income Distributions with Applications," Econometrica, Econometric Society, vol. 48(7), pages 1791-1803, November.
    3. Thomas Piketty & Emmanuel Saez, 2006. "The Evolution of Top Incomes: A Historical and International Perspective," American Economic Review, American Economic Association, vol. 96(2), pages 200-205, May.
    4. Singh, S K & Maddala, G S, 1978. "A Function for Size Distribution of Incomes: Reply," Econometrica, Econometric Society, vol. 46(2), pages 461-461, March.
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    Cited by:

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    3. Thomas Blanchet & Lucas Chancel & Amory Gethin, 2022. "Why Is Europe More Equal than the United States?," American Economic Journal: Applied Economics, American Economic Association, vol. 14(4), pages 480-518, October.
    4. Demetrio Guzzardi & Elisa Palagi & Andrea Roventini & Alessandro Santoro, 2022. "Reconstructing Income Inequality in Italy: New Evidence and Tax Policy Implications from Distributional National Accounts," SciencePo Working papers Main halshs-03693201, HAL.
    5. Carranza, Rafael & De Rosa, Mauricio & Flores, Ignacio, 2023. "Wealth inequality in Latin America," LSE Research Online Documents on Economics 119426, London School of Economics and Political Science, LSE Library.
    6. Thomas Blanchet & Ignacio Flores & Marc Morgan, 2022. "The weight of the rich: improving surveys using tax data," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 20(1), pages 119-150, March.
    7. Andrea Fontanari & Nassim Nicholas Taleb & Pasquale Cirillo, 2017. "Gini estimation under infinite variance," Papers 1707.01370, arXiv.org, revised Dec 2017.
    8. Nassim Nicholas Taleb, 2015. "How to (Not) Estimate Gini Coefficients for Fat Tailed Variables," Papers 1510.04841, arXiv.org.
    9. Maia, Adriano & Matsushita, Raul & Da Silva, Sergio, 2020. "Earnings distributions of scalable vs. non-scalable occupations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
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    11. Pablo Gutiérrez Cubillos, 2022. "Gini and undercoverage at the upper tail: a simple approximation," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 29(2), pages 443-471, April.
    12. Ignacio Flores, 2021. "The capital share and income inequality: Increasing gaps between micro and macro-data," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 19(4), pages 685-706, December.

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    More about this item

    Keywords

    Quantile contribution; Measure of inequality; Estimation bias; Power law; Law of large number; Concentration measure;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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